Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 781: 52


$$\frac{\partial P}{\partial V}=-\frac{nRT}{V^2},$$ $$\frac{\partial P}{\partial T}= \frac{nR}{V}.$$

Work Step by Step

Since $ P=\frac{nRT}{V}=nRTV^{-1}$, then we have $$\frac{\partial P}{\partial V}=-nRTV^{-2}=-\frac{nRT}{V^2},$$ $$\frac{\partial P}{\partial T}=nRV^{-1}= \frac{nR}{V}.$$
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